Thread: confused

my math teacher said everything to the zero power is one

BUT,


does infinity^(0) = 0 bcause 1/infinity = 0 and infinity^(1) = infinity
0 x infinity = 0

It's hard to make infinity fit into our everyday arithmetic. Some operations have natural definitions--infinity plus any number is infinity, for example, or infinity times any positive number is infinity--but when you try to extend things in every single direction, you're bound to run into some trouble. For example, what should infinity minus infinity be? If we say 0, then what about:

1 = 1 + (infinity - infinity) = (1+infinity) - infinity = infinity - infinity = 0

Uh oh, that's really bad.

The solution is this. If we're very careful what we mean by infinity and what we intend to do with it, then we can often make sense out of arithmetic expressions involving infinity. But if we just try to squeeze infinity into our basic notions of arithmetic without describing the context, we're just going to confuse ourselves.

Cool?

just remember that infinity is not a number, so does not react to arithmetic operations as a number would
after all, no number remains unchanged when you take a non-zero number away from it

(infinity - 1 = infinity
x - 1 != x)

Originally Posted by mathformonkeys

my math teacher said everything to the zero power is one

BUT,


does infinity^(0) = 0 bcause 1/infinity = 0 and infinity^(1) = infinity
0 x infinity = 0

As the others have said, context is everything, and we cannot assume that operations we perform on the counting numbers are operations we can perform on other types of numbers: infinity, 0 itself and i, for instance, need to have specially defined rules and restrictions upon their operations.

It is why, for example, you cannot make arithmetic sense of n/0 - it's just not allowed to do that except by using the concept of a limit, in which case you are not literally dividng a number by 0.